• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.41-51
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• 2007

Let R be a ring with left identity e and suitably-restricted additive torsion, and Z(R) its center. Let H : $R{\times}R{\times}R{\rightarrow}R$ be a symmetric 3-additive mapping, and let h be the trace of H. In this paper we show that (i) if for each $x{\in}R$, $$n=<<\cdots,\;x>,\;\cdots,x>{\in}Z(R)$$ with $n\geq1$ fixed, then h is commuting on R. Moreover, h is of the form $$h(x)=\lambda_0x^3+\lambda_1(x)x^2+\lambda_2(x)x+\lambda_3(x)\;for\;all\;x{\in}R$$, where $\lambda_0\;{\in}\;Z(R)$, $\lambda_1\;:\;R{\rightarrow}R$ is an additive commuting mapping, $\lambda_2\;:\;R{\rightarrow}R$ is the commuting trace of a bi-additive mapping and the mapping $\lambda_3\;:\;R{\rightarrow}Z(R)$ is the trace of a symmetric 3-additive mapping; (ii) for each $x{\in}R$, either $n=0\;or\;<n,\;x^m>=0$ with $n\geq0,\;m\geq1$ fixed, then h = 0 on R, where denotes the product yx+xy and Z(R) is the center of R. We also present the conditions which implies commutativity in rings with identity as motivated by the above result.

• Korean Journal of Food Science and Technology
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• v.52 no.6
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• pp.587-594
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• 2020

In this study, we analyzed glucosinolates and their metabolites in the inner and outer parts of napa cabbage (NC; Brassica rapa subsp. pekinensis) and napa cabbage kimchi (NKC) using UPLC-ESI-MS/MS. In the extracts from NC and NKC, glucobrassicanapin (m/z 386), glucoalyssin (m/z 450), glucobrassicin (m/z 447), 4-methoxyglucobrassicin (m/z 477), and neoglucobrassicin (m/z 477) were detected using the MS scan mode ([M-H]-), and gluconapin (m/z 372→97), progoitrin (m/z 388→97), glucoiberin (m/z 422→97), 4-methoxyglucobrassicin (m/z 477→97), and neoglucobrassicin (m/z 477→447) were detected using the MS/MS MRM mode ([M-H]-). Ascorbigen (m/z 306→130) and indole-3-carboxaldehyde (I3A; m/z 146→118), which were metabolites of glucobrassicins, were detected using the MS/MS MRM ([M+H]+) mode. The peak intensities of ascorbigen in the extract from the inner and outer parts of NC were significantly higher than those of the NKC extract (p<0.05); however, there was no significant difference in I3A peak intensity between the NC and NKC extracts.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.105-123
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• 2015

Let $f_{\beta}=h_{\beta}+\bar{g}_{\beta}$ and $F_a=H_a+\bar{G}_a$ be harmonic mappings obtained by shearing of analytic mappings $h_{\beta}+g_{\beta}=1/(2isin{\beta})log\((1+ze^{i{\beta}})/(1+ze^{-i{\beta}})\)$, 0 < ${\beta}$ < ${\pi}$ and $H_a+G_a=z/(1-z)$, respectively. Kumar et al. [7] conjectured that if ${\omega}(z)=e^{i{\theta}}z^n({\theta}{\in}\mathbb{R},n{\in}\mathbb{N})$ and ${\omega}_a(z)=(a-z)/(1-az)$, $a{\in}(-1,1)$ are dilatations of $f_{\beta}$ and $F_a$, respectively, then $F_a\tilde{\ast}f_{\beta}{\in}S^0_H$ and is convex in the direction of the real axis, provided $a{\in}[(n-2)/(n+2),1)$. They claimed to have verified the result for n = 1, 2, 3 and 4 only. In the present paper, we settle the above conjecture, in the affirmative, for ${\beta}={\pi}/2$ and for all $n{\in}\mathbb{N}$.

• Journal of Microbiology and Biotechnology
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• v.11 no.4
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• pp.649-655
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• 2001

The kinetics of the thermolysin-catalyzed synthesis of N-(benzyloxycarbonyl)-L-phenylalanyl-L-leucine ethyl ester (Z-Phe-LeuOEt) from N-(benzyloxycarbonyl)-L-phyenylalanine (Z-Phe) and L-leucine ethyl ester (LeuOEt) in an ethyl acetate saturated aqueous system in a batch operation were studied. The kinetics for the synthesis of Z-Phe-LeuOEt were expressed using a rate equation for the rapid equilibrium random bireactant mechanism. The four kinetic constants involved in the rate equation were determined numerically by the quasi-Newton method so as to fit the calculated results with the experimental data. Within the pH and temperature range examined, the $K_{cat}$ value for the synthesis of Z-Phe-LeuOEt reached a maximum at pH 7.0 and $45^{\circ}C$, whereas the affinity between Z-Phe and thermolysin reached a maximum at pH 6.0 adn $40^{\circ}C$. The inhibitory effect of Z-Phe on the condensation reaction decreased as the pH and temperature decreased. In contrast, they affinity between LeuOEt and thermolysin remained unchanged within the pH and temperature range examined. Therefore, it was concluded that the protonation state of the carboxyl groups. of Z-Phe was more imprtant than that of the amono groups of LeuOEt for the synthesis of Z-Phe-LeuOEt in the present solvent system. The equilibrium yield at pH 6.0 and $30^{\circ}C$ was 8% higher than that at pH 7.0 and $40^{\circ}C$, although the rate was much slower. This result suggested that the affinity between the enzyme and the substrate rather than the overall rate was a more important factor affecting the equilibrium yield, when the peptide synthesis was carried out in a product-precipitation system.

• Bulletin of the Korean Chemical Society
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• v.33 no.9
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• pp.3039-3042
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• 2012

Pressure tensors at the planar surface of liquid-vapor argon are evaluated from the virial theorem, Irving-Kirkwood, and Harasima versions using a test-area molecular dynamics simulation method through a Lennard-Jones intermolecular potential at two temperatures. We found that the normal and transverse components of the pressure tensor, $p_N(z)$ and $p_T(z)$, obtained from the virial theorem and Harasima version are essentially the same. The normal component of the pressure tensor from Irving-Kirkwood version, $p_N^{IK}(z)$, is shown to be a nearly constant at the lower temperature, independent of z, as agreed in a previous study, but not for $p_N^H$(z), while the transverse components, $p_T^{IK}(z)$ and $p_T^H(z)$, are almost the same. The values of surface tension for both versions computed from $p_N(z)-p_T(z)$ are also the same and are fully consistent with the experimental data.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.65-74
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• 2007

Suppose that $\mu$ is a finite positive Borel measure on bounded symmetric domain $\Omega{\subset}\mathbb{C}^n\;and\;\nu$ is the Euclidean volume measure such that $\nu(\Omega)=1$. Suppose 1 < p < $\infty$ and r > 0. In this paper, we will show that the norms $sup\{\int_\Omega{\mid}k_z(w)\mid^2d\mu(w)\;:\;z\in\Omega\}$, $sup\{\int_\Omega{\mid}h(w)\mid^pd\mu(w)/\int_\Omega{\mid}h(w)^pd\nu(w)\;:\;h{\in}L_a^p(\Omega,d\nu),\;h\neq0\}$ and $$sup\{\frac{\mu(E(z,r))}{\nu(E(z,r))}\;:\;z\in\Omega\}$$ are are all equivalent. We will also show that the inclusion mapping $ip\;:\;L_a^p(\Omega,d\nu){\rightarrow}L^p(\Omega,d\mu)$ is compact if and only if lim $w\rightarrow\partial\Omega\frac{\mu(E(w,r))}{\nu(E(w,r))}=0$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.247-260
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• 2011

Let h be a meromorphic function with few poles and zeros. By Nevanlinna's value distribution theory we prove some new properties on the polynomials in h with the coefficients being small functions of h. We prove that if f is a meromorphic function and if $f^m$ is identically a polynomial in h with the constant term not vanish identically, then f is a polynomial in h. As an application, we are able to find the entire solutions of the differential equation of the type $$f^n+P(f)=be^{sz}+Q(e^z)$$, where P(f) is a differential polynomial in f of degree at most n-1, and Q($e^z$) is a polynomial in $e^z$ of degree k $\leqslant$ max {n-1, s(n-1)/n} with small functions of $e^z$ as its coefficients.

• Korean Journal of Crystallography
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• v.5 no.2
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• pp.108-112
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• 1994

C19H20O5, Mr=314.337, triclinic,PI, a=10.291(2)A, b=11.218(3)A, c=3.059(1)A, α=74.54(2)°, β=1148.84(1)°, r=109.84(2)°, V=883.283(2)A3, λ(Mo Kα)=0.71069A, μ=0.47 mm-1, F(000)=324, 296K, Z=2, Dx=1.18Mgm-3. Final R=0.0580 for 1637[F>3σ(F)]unique refledtions. α,β-diphenylsuccinic acid, C16H14O4, are connedted with the solvent actone by hydrogen bond O(4)-H˙˙˙O(5), forming a dimer related by related by centrosymmentry thorough intermolecualr carboxylic hydrogen bond O(1)-H˙˙˙O(2)(-x,-y,-z). The nearest distance 3.288A[O(2)˙˙˙O(2)(-x,-y,-z)] between the dimers shows that the packing of the dimer is govermed by van der Waals'force.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.911-927
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• 2019

Let $\mathscr{B}^{{\eta},{\mu}}_{p,n}\;({\alpha});\;({\eta},{\mu}{\in}{\mathbb{R}},\;n,\;p{\in}{\mathbb{N}})$ denote all functions f class in the unit disk ${\mathbb{U}}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: $$\|\[{\frac{f^{\prime}(z)}{pz^{p-1}}}\]^{\eta}\;\[\frac{z^p}{f(z)}\]^{\mu}-1\| <1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. And $\mathscr{M}^{{\eta},{\mu}}_{p,n}\;({\alpha})$ indicates all meromorphic functions h in the punctured unit disk $\mathbb{U}^*$ as $h(z)=z^{-p}+\sum_{k=n-p}^{\infty}b_kz^k$ which satisfy: $$\|\[{\frac{h^{\prime}(z)}{-pz^{-p-1}}}\]^{\eta}\;\[\frac{1}{z^ph(z)}\]^{\mu}-1\|<1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. In this paper several sufficient conditions for some classes of functions are investigated. The authors apply Jack's Lemma, to obtain this conditions. Furthermore, sufficient conditions for strongly starlike and convex p-valent functions of order ${\gamma}$ and type ${\beta}$, are also considered.

• Journal of Microbiology
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• v.34 no.4
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• pp.327-333
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• 1996

Yeast, like many other microbes, encounters large variations in ambient pH in their natural environments. Microorganisms capable of growing over a wide pH range require a versatile, efficient pH homeostatic mechanism protecting intracellular processes against extremes of pH. In several organisms, fusions to the bacterial lacZ gene have been extremely useful for the identification of genes expressed at different time during the life cycle or under different growth conditions. In this study, using the lacZ gene screening system, we surveyed a large number of yeast strains with lacZ insertion to identify genes regulated by pH. A yeast genomic library was constructed and inserted with lacZ by a shuttle mutagenesis procedure. The yeast transformants were individually picked up with a toothpick, replica-plated, and grown in alkaline pH medium. Among the 35,000 colonies screened, 10 candidate strains were identified initially by the $\beta$-gal assay. We finally confirmed two yeast strains carrying the genes whose expression are strictly dependent on pH of growth medium. One of the fusions showing a 10-fold induction in expression level in response to alkali pH was selected and further characterized. The pH-regulated gene was cloned by inverse PCR and a partial sequence of the gene was determined. Identification and characterization of the gene is currently under investigation.